User:Inthar/4L 3s: Difference between revisions

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Line 97: Line 97:
! class="unsortable"|Degree
! class="unsortable"|Degree
! [[18edo]] (soft)
! [[18edo]] (soft)
! [[25edo]] (supersoft)
! [[43edo]]
! class="unsortable"| Note name on J
! class="unsortable"| Note name on J
! class="unsortable"| Approximate ratios
! class="unsortable"| Approximate ratios
Line 105: Line 103:
| | unison
| | unison
| 0\18, 0.0
| 0\18, 0.0
| 0\25, 0.0
| 0\43, 0.0
| J
| J
| 1/1
| 1/1
Line 113: Line 109:
| chroma
| chroma
| 1\18, 66.7
| 1\18, 66.7
| 1\25, 48.0
| 2\43, 55.8
| J&
| J&
|  
|  
Line 121: Line 115:
| dim. mos2nd
| dim. mos2nd
| 1\18, 66.7
| 1\18, 66.7
| 2\25, 96.0
| 3\43, 83.7
| K@@
| K@@
|  
|  
Line 129: Line 121:
| minor mos2nd
| minor mos2nd
| 2\18, 133.3
| 2\18, 133.3
| 3\25, 144.0
| 5\43, 139.5
| K@
| K@
| 13/12
| 13/12
Line 137: Line 127:
| major mos2nd
| major mos2nd
| 3\18, 200.0
| 3\18, 200.0
| 4\25, 192.0
| 7\43, 195.3
| K
| K
| 9/8, 10/9
| 9/8, 10/9
Line 145: Line 133:
| aug. mos2nd
| aug. mos2nd
| 4\18, 266.7
| 4\18, 266.7
| 5\25, 240.0
| 9\43, 251.2
| K&
| K&
|  
|  
Line 153: Line 139:
| dim. mos3rd
| dim. mos3rd
| 4\18, 266.7
| 4\18, 266.7
| 6\25, 288.0
| 10\43, 279.1
| L@
| L@
|  
|  
Line 161: Line 145:
| perf. mos3rd
| perf. mos3rd
| 5\18, 333.3
| 5\18, 333.3
| 7\25, 336.0
| 12\43, 334.9
| L
| L
| 17/14, 40/33
| 17/14, 40/33
Line 169: Line 151:
| aug. mos3rd
| aug. mos3rd
| 6\18, 400.0
| 6\18, 400.0
| 8\25, 384.4
| 14\43, 390.7
| L&
| L&
| 5/4
| 5/4
Line 177: Line 157:
| doubly aug. mos3rd
| doubly aug. mos3rd
| 7\18, 466.7  
| 7\18, 466.7  
| 9\25, 432.0
| 16\43, 446.5
| L&&
| L&&
|  
|  
Line 185: Line 163:
| dim. mos4th
| dim. mos4th
| 6\18, 400.0
| 6\18, 400.0
| 9\25, 432.0
| 15\43, 418.6
| M@@
| M@@
|  
|  
Line 193: Line 169:
| minor mos4th
| minor mos4th
| 7\18, 466.7
| 7\18, 466.7
| 10\25, 480.0
| 17\43, 474.4
| M@
| M@
| 21/16
| 21/16
Line 201: Line 175:
| major mos4th
| major mos4th
| 8\18, 533.3  
| 8\18, 533.3  
| 11\25, 528.0
| 19\43, 530.2
| M
| M
| 19/14, 34/25
| 19/14, 34/25
Line 209: Line 181:
| aug. mos4th
| aug. mos4th
| 9\18, 600.0
| 9\18, 600.0
| 12\25, 576.0
| 21\43, 586.0
| M&
| M&
| 7/5
| 7/5
Line 217: Line 187:
| dim. mos5th
| dim. mos5th
| 9\18, 600.0
| 9\18, 600.0
| 13\25, 624.0
| 22\43, 614.0
| N@
| N@
| 10/7
| 10/7
Line 225: Line 193:
| minor mos5th
| minor mos5th
| 10\18, 666.7
| 10\18, 666.7
| 14\25, 672.0
| 24\43, 669.8
| N
| N
| 28/19, 25/17
| 28/19, 25/17
Line 233: Line 199:
| major mos5th
| major mos5th
| 11\18, 733.3
| 11\18, 733.3
| 15\25, 720.0
| 26\43, 725.6
| N&
| N&
| 32/21
| 32/21
Line 241: Line 205:
| aug. mos5th
| aug. mos5th
| 12\18, 800.0
| 12\18, 800.0
| 16\25, 768.0
| 28\43, 781.4
| N&&
| N&&
|  
|  
Line 249: Line 211:
| doubly dim. mos6th
| doubly dim. mos6th
| 11\18, 733.3
| 11\18, 733.3
| 16\25, 768.0
| 27\43, 753.5
| O@@
| O@@
|  
|  
Line 257: Line 217:
| dim. mos6th
| dim. mos6th
| 12\18, 800.0
| 12\18, 800.0
| 17\25, 816.0
| 29\43, 809.3
| O@
| O@
| 8/5
| 8/5
Line 265: Line 223:
| perf. mos6th
| perf. mos6th
| 13\18, 866.7
| 13\18, 866.7
| 18\25, 864.0
| 31\43, 865.1
| O
| O
| 28/17, 33/20
| 28/17, 33/20
Line 273: Line 229:
| aug. mos6th
| aug. mos6th
| 14\18, 933.3
| 14\18, 933.3
| 19\25, 912.0
| 33\43, 920.9
| O&
| O&
|  
|  
Line 281: Line 235:
| dim. mos7th
| dim. mos7th
| 14\18, 933.3
| 14\18, 933.3
| 20\25, 960.0
| 34\34, 948.8
| P@
| P@
|  
|  
Line 289: Line 241:
| minor mos7th
| minor mos7th
| 15\18, 1000.0
| 15\18, 1000.0
| 21\25, 1008.0
| 36\43, 1004.7
| P
| P
| 16/9, 9/5
| 16/9, 9/5
Line 297: Line 247:
| major mos7th
| major mos7th
| 16\18, 1066.7
| 16\18, 1066.7
| 22\25, 1056.0
| 38\43, 1060.5
| P&
| P&
| 24/13
| 24/13
Line 305: Line 253:
| aug. mos7th
| aug. mos7th
| 17\18, 1133.3
| 17\18, 1133.3
| 23\25, 1104.0
| 40\43, 1116.3
| P&
| P&
|  
|  
Line 313: Line 259:
| dim. mosoctave
| dim. mosoctave
| 17\18, 1133.3
| 17\18, 1133.3
| 24\25, 1152.0
| 41\43, 1144.2
| J@
| J@
|  
|  

Revision as of 05:01, 29 April 2021

11edo smitonic

The intervals of the symmetric LsLsLsL mode (harmonics in bold):

Degree (1 = tonic) Cents Note name on C (22edo notation) Approximate ratios #Gens up
1 0 C 1/1 0
2 218.18 D 8/7, 9/8, 17/15 -3
3 327.27 Eb^ 6/5, 11/9, 17/14 +1
4 545.45 F^ 11/8, 15/11 -2
5 654.54 Gv 16/11, 22/15 +2
6 872.72 Av 5/3, 18/11, 28/17 -1
7 981.81 Bb 7/4, 16/9, 30/17 +3

Assuming the symmetric 2121212 mode, the 1-4-7 chord is:

  • 8:11:14 on degrees 1 and 6
  • 8:11:15 on degrees 3, 5, and 7
  • (something complex) on degrees 2 and 4

Modal harmony

Main article: Smitonic

The seven modes are, from brightest to darkest:

Nerevarine mode LLSLSLS
Vivecan mode LSLLSLS
Lorkhanic mode LSLSLLS
Sothic mode LSLSLSL
Kagrenacan mode SLLSLSL
Almalexian mode SLSLLSL
Dagothic mode SLSLSLL

Modally, the highest to lowest entropy scale degrees (unison = 1) are:

  • 2 and 7 (equally): .99 bits
  • 4 and 5 (equally): .86 bits
  • 3 and 6 (equally): .59 bits

If a scale degree is high entropy it tends to be the most informative on average; the modes that have this interval as major and minor respectively are roughly a 50-50 split. This tells us that unlike in the diatonic scale, thirds and sixths are the least informative in distinguishing smitonic modes. On the other hand, seconds, fourths and sevenths are highly informative.

In orgone, these scale degrees appear in the most consonant triads and tetrads of 11edo orgone, namely 8:9:11:15, 8:9:11:14 and 16:17:22:28. Those chords are therefore crucial for Orgone[7] modal harmony.

18edo smitonic

Degree 18edo (soft) Note name on J Approximate ratios #Gens up
unison 0\18, 0.0 J 1/1 0
chroma 1\18, 66.7 J& -7
dim. mos2nd 1\18, 66.7 K@@ +11
minor mos2nd 2\18, 133.3 K@ 13/12 +4
major mos2nd 3\18, 200.0 K 9/8, 10/9 -3
aug. mos2nd 4\18, 266.7 K& -10
dim. mos3rd 4\18, 266.7 L@ +8
perf. mos3rd 5\18, 333.3 L 17/14, 40/33 +1
aug. mos3rd 6\18, 400.0 L& 5/4 -6
doubly aug. mos3rd 7\18, 466.7 L&& -13
dim. mos4th 6\18, 400.0 M@@ +12
minor mos4th 7\18, 466.7 M@ 21/16 +5
major mos4th 8\18, 533.3 M 19/14, 34/25 -2
aug. mos4th 9\18, 600.0 M& 7/5 -9
dim. mos5th 9\18, 600.0 N@ 10/7 +9
minor mos5th 10\18, 666.7 N 28/19, 25/17 +2
major mos5th 11\18, 733.3 N& 32/21 -5
aug. mos5th 12\18, 800.0 N&& -12
doubly dim. mos6th 11\18, 733.3 O@@ +13
dim. mos6th 12\18, 800.0 O@ 8/5 +6
perf. mos6th 13\18, 866.7 O 28/17, 33/20 -1
aug. mos6th 14\18, 933.3 O& -8
dim. mos7th 14\18, 933.3 P@ +10
minor mos7th 15\18, 1000.0 P 16/9, 9/5 +3
major mos7th 16\18, 1066.7 P& 24/13 -4
aug. mos7th 17\18, 1133.3 P& -11
dim. mosoctave 17\18, 1133.3 J@ +7

Modal harmony

MODMOSes and chroma modification become more important...

Treat it as neutralized mavila antidiatonic?

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